Retardance measurement system and method

ABSTRACT

In an apparatus and method for measuring retardance and slow axis azimuth in sample specimens, a sample is illuminated by circularly polarized monochromatic light which is then analyzed by an elliptical analyzer at different settings. In another embodiment, light conditioned by an elliptical polarizer at various settings illuminates a specimen and the beam exiting the sample is analyzed by a circular analyzer. The elliptical analyzer/polarizer may have selectable ellipticity and azimuth angle, including in some cases a setting of circular polarization. Background images obtained with selected settings of the elliptical analyzer/polarizer, but without the sample present, are used in some embodiments to improve the measurement.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is related to polarized light and, moreparticularly, to measurement of retardance and slow axis azimuth angle,and most especially to systems that produce images of these propertiesin a two-dimensional image of a sample.

2. Description of the Related Art

Measuring of two-dimensional birefringence distributions is anestablished technique for analyzing the structure of various specimens.It can also be applied to study the vector or tensor fields associatedwith birefringence.

The application of two-dimensional birefringence measurements to theanalysis of inner stress in construction models using photoelasticity isalso well known (Handbook on Experimental Mechanics, Ed. by Albert S.Kobayashi, Prentice Hall: Englewood Cliffs, 1987). E. A. Patterson andco-authors offered a full-field imaging polariscope (E. A. Patterson, W.Ji, and Z. Fwang, “On Image Analysis For Birefringence Measurements inPhotoelasticity”, Optic Laser Engineering, 28, pp. 17–36, 1997). It hasa circularly polarized illumination beam and six consecutive settings ofan analyzer polarizer: left and right circular polarized settings andfour linear polarized settings at 0°, 45°, 90° and 135°.

The technique doesn't provide high sensitivity with low retardancespecimens, and describes use of a polarization state analyzer comprisinga rotated quarter waveplate and rotated linear analyzer.

Imaging polarization techniques have been important for microscopestudies of biological specimens (S. Inoué, “A Method For Measuring SmallRetardations of Structures in Living Cells”, Exp. Cell Res. 2,pp.513–517, 1951; S. Inoue and K. R. Spring, Video Microscopy. TheFundamentals, 2 _(nd) ed., New York: Plenum Press, 1997; S. Inoué and R.Oldenbourg, Microscopes, in Handbook of Optics, M. Bass, Editor. 1995,McGraw-Hill, Inc.: New York. pp. 17.1–17.52).

Other systems for imaging measurement systems with rotated opticalpolarization elements have been shown (M. Noguchi, T. Ishikawa, M. Ohno,and S. Tachihara, “Measurement of 2D Birefringence Distribution,” inInternational Symposium on Optical Fabrication, Testing, and SurfaceEvaluation, Jumpei Tsujiuchi, ed., Proc. SPIE 1720, 367–378,1992; Y.Otani, T. Shimada, T. Yoshizawa, “The Local-Sampling Phase ShiftingTechnique For Precise Two-Dimensional Birefringence Measurement”,Optical Review, 1(1), pp.103–106, 1994).

J. L. Pezzanitti, and R. A. Chipman proposed a device for measuringMuller matrix coefficients, comprising a polarization state generatorand polarization state analyzer. (J. L. Pezzanitti, and R. A. Chipman,“Mueller Matrix Imaging Polarimetry”, Opt. Eng. 34(6), pp.1558–1568,1995). The generator and analyzer are created by fixed linear polarizerswith parallel transmittance axes and two waveplates, which are rotatedwith a 5:1 ratio. The waveplate retardances are the same, equal toone-quarter or one-third wavelength. At least 25 consecutive images arerequired in order to determine a Muller matrix, and in the example giventhe authors acquire a total of 60 images per measurement.

Y. Zhu and coauthors described two-dimensional techniques forbirefringence measurement (Y. Zhu, T. Koyama, T. Takada, and Y. Murooka,“Two-Dimensional Measurement Technique For Birefringence VectorDistributions: Measurement Principle,” Appl. Opt. 38, pp. 2225–2231,1999). A specimen is illuminated by a beam at three polarization states:one linearly polarized and two elliptically polarized with the sameellipticity value and opposite ellipticity sign, which are obtained bymechanically rotated optical elements. A total of six images are used toobtain the two-dimensional retardance and slow axis azimuthdistribution.

A birefringence-mapping device, which contains a mechanically rotatedlinear polarizer and circular analyzer was described by Glazier andCosier in 1997 (A. M. Glazer, and J. Cosier, “Method and Apparatus ForIndicating Optical Anisotropy,” UK Patent Application No. 2,310,925).Typically, six images of a specimen are taken while the linear polarizeris incremented in 30° steps; these images. are then processed to yieldthe birefringence map, as described in an article (A. M. Glazer, J. G.Lewis, and W. Kaminsky, “An Automatic Optical Imaging System ForBirefringent Media,” Proc. R. Soc. Lond. A 452, pp. 2751–2765, 1996).The device is not suitable for measuring low retardance specimensbecause it is strongly susceptible to light intensity variations, photonstatistical noise, detector read-out noise, and digitization error.

Devices with return-path techniques have also been described, by M. I.Shribak “Autocollimating Detectors of Birefringence”, in InternationalConference on Optical Inspection and Micromeasurements, ChristopheGorecki, Editors, Proc.SPIE 2782, pp.805–813, 1996; and by M. I.Shribak, Y. Otani and T. Yoshizawa, “Return-Path Polarimeter For TwoDimensional Birefringence Distribution Measurement”, Polarization:Measurement, Analysis, and Remote Sensing II, Dennis H., Goldstein; andDavid B. Chenault; Eds. Proc., SPIE 3754, pp. 144–149, 1999.

R. Oldenbourg and G. Mei described a method for measurement ofretardance and slow-axis azimuth distribution using two techniques:three elliptical and one circular polarized state of illumination beamand circular analyzer; circular polarized state of illumination beam andthree consecutive elliptical and one circular polarized setting ofanalyzer in “Polarized Light Microscopy,” U.S. Pat. No. 5,521,705.

R. Oldenbourg describes a background correction procedure in “RetardanceMeasurement Method,” U.S. Pat. No. 6,501,548. The method is based onusing a universal compensator as an elliptical polarizer/analyzer whichis formed by a pair of variable liquid crystal retarders and a linearpolarizer.

While there have thus been shown various techniques for retardancemeasurement and two-dimensional retardance imaging, the existingtechniques in the art require taking six or more readings; or are notwell-suited to measurement of low-retardance samples; or do not operatewith high speed; or offer less than adequate accuracy or noise.

SUMMARY OF THE INVENTION

The present invention provides apparatus and methods for measuringretardance and principal plane azimuth distribution in samples. Itprovides for unsurpassed accuracy and low noise in one embodiment, whichrequires 4 or 5 intensity readings per measurement. In anotherembodiment, it provides a measurement of retardance and principal planeazimuth distribution from as few as two or three specimen readingstogether with background readings that are taken once and need not berepeated with each measurement. Thus the present invention provides fullinformation about retardance and azimuth angle with improved noise thanthe prior art, or with fewer readings required per measurement, or both.It is well-suited for use with an imaging detector to producetwo-dimensional retardance images of a specimen. These and other aspectsof the invention will be clear from the description provided below.

In accordance with the invention, a specimen is illuminated bycircularly polarized monochromatic light and the beam exiting thespecimen is analyzed with an elliptical analyzer at different settings,and its intensity is noted. In another embodiment light conditioned byan elliptical polarizer at different settings illuminates a specimen andthen passes through a circular analyzer and its intensity is measured.The elliptical analyzer/polarizer can change the degree of ellipticityand azimuth angle, including a setting with circular polarization. Inaddition, the invention includes the step of taking images at the samesettings of the elliptical analyzer/polarizer without the specimenpresent, for purposes of background correction.

The invention uses the following novel algorithms to produce retardancemeasurements:

two specimen images with elliptical settings and three or two backgroundimages;

three specimen images with elliptical settings;

four specimen images with elliptical settings without extinctionsetting;

five specimen images with four elliptical settings and one extinctionsetting.

These algorithms allow one to optimize the measurement for speed,sensitivity, and accuracy. The highest accuracy can be achieved usingthe 5-frame technique, and in the 4-frame algorithm without extinctionsetting. Alternatively, when high acquisition speed is important, aswhen imaging a moving sample, the two-frame algorithm or three-framealgorithm is valuable.

These various algorithms can be employed for polarization imagingsystems using different optical configurations to produce the required,elliptical and/or circular illumination and analyzer functions. Suitableapparatus for practicing the invention includes variable retarders suchas liquid crystal and electro optical waveplates; waveplates withvariable azimuth; fixed waveplates such as quartz or polymer retardersthat are mechanically engaged or re-oriented as needed; Faradayrotators; and, indeed, any optical element that performs the requiredfunction can be employed. The choice of one optical element over anotherwill be made according to the requirements of the application at handfor measurement speed, size, accuracy, cost, complexity, and otherdesign criteria that may be relevant.

Although the invention is described with specific reference to its usein microscope systems, it can be practiced using a variety of opticalsystems and is not inherently limited or restricted to use with smallsamples or in microscopy settings. It can be operated with samples thatare viewed in transmission or in reflection. Similarly, although specialattention is paid to producing a two-dimensional retardance map, forwhich the invention is well-suited, the invention can be practiced whena lesser number of retardance measures are needed, or even a singlepoint needs to be measured. Indeed, it is specifically intended that thepresent invention may be practiced in any context in which it is usefulto measure retardance in a sample. Accordingly, it is intended thatwherever this description speaks of taking a specimen image (to denote ameasurement of intensity across a two-dimensional image), one shouldunderstand that it is also possible to implement a comparable systemthat takes a single point measurement of intensity, or a measurement ofintensity at a plurality of points in a line, or a measurement ofintensity in any spatial format that is of interest for a givenapplication; and similarly, whenever this description speaks of takingan intensity reading, one should understand that to mean a single pointreading of intensity, a two-dimensional image of intensity, or ameasurement of intensity in any spatial format that is of interest.

The various features of novelty which characterize the invention arepointed out with particularity in the claims annexed to and forming apart of the disclosure. For a better understanding of the invention, itsoperating advantages, and specific objects attained by its use,reference should be had to the drawing and descriptive matter in whichthere are illustrated and described preferred embodiments of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, wherein like reference characters denote similarelements throughout the various Figures:

FIG. 1 is a schematic drawing implementing the invention in a firstoptical arrangement to construct the variable elliptical polarizers;

FIG. 2 is a schematic drawing implementing the invention in a secondoptical arrangement to construct the variable elliptical polarizers;

FIG. 3 is a schematic drawing of probe beam settings on the Poincaresphere, in which χ₀ is the setting with right circular polarization, andχ₁, χ₂, χ₃, and χ₄ are settings with elliptical polarizations;

FIG. 4 is a table illustrating examples of polarization settings of theprobe beam with ellipticity ε and major axis azimuth γ and thecorresponding retardances α and β of liquid crystal plates 114 and 115whose optical axes 116 and 117 are oriented at angles of 45° and 22.5°to each other, respectively;

FIG. 5 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for birefringencemapping using the two-image algorithm;

FIG. 6 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for backgroundbirefringence mapping using the three-image algorithm;

FIG. 7 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for specimenbirefringence mapping using the three-image algorithm;

FIG. 8 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for backgroundbirefringence mapping using the four-image algorithm;

FIG. 9 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for specimenbirefringence mapping using the four-image algorithm;

FIG. 10 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for backgroundbirefringence mapping using the five-image algorithm; and

FIG. 11 is a simplified flow-chart illustrating a sequence of ellipticalpolarizer settings used with the apparatus of FIG. 1 for specimenbirefringence mapping using the five-image algorithm.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

Optical configurations suitable for practicing the invention in amicroscope are shown in schematic form in FIG. 1. The apparatus consistsof the following elements in series: monochromatic light source 101, avariable elliptical polarizer 102, a condenser 103, the specimen 104, anobjective lens 105, a right or left circular analyzer 106 comprisingquarter waveplate 107 with retardance of λ/4 and fast axis at azimuthangle of ±45° and linear analyzer 109 with a transmission axis atazimuth angle of 0°, and imaging detector 111. The detector andpolarizer are in communication with processor 119, which receives thephotodetector signals and performs the calculations of retardance; andoptional display 120, which provides images of the retardance to anoperator or user.

The monochromatic light source may operate in the visible, theultraviolet, or the infrared, according to what is desired. The detectorand other elements should be responsive in the selected wavelength band,as is known to those skilled in the art. In this context, monochromaticmeans a narrow range of wavelengths, but need not be literally a singlewavelength such as a laser emits. A broadband lamp and filter may beused successfully.

Another set of optical configurations suitable for practicing theinvention is shown in schematic form in FIG. 2. These consist of anilluminator 101, a right or left circular polarizer 106 comprisinglinear polarizer 109 with transmission axis at azimuth angle of 0° andquarter waveplate 107 with retardance λ/4 and fast axis azimuth at ±45°sample 106, objective lens 105, and a variable elliptical analyzer 102in the imaging path.

The variable elliptical polarizer 102 is further made up from liquidcrystal retarder cells 114 and 115, adjacent a linear polarizer 118. Inthe apparatus of FIG. 1, the angle between the polarizer transmissionaxis and the crystal axis of retarder 114 is +/−45°, and between thecrystal axis of retarder 114 and the crystal axis of retarder 115 is+/−45°. In the apparatus of FIG. 2, the angle between the polarizertransmission axis and the crystal axis of retarder 114 is +/−22.5° or+/−67.5°, and the angle between the crystal axis of retarder 114 and thecrystal axis of retarder 115 is +/−22.5° or +/−67.5°.

While here and throughout this disclosure these angles and retardancesare specified precisely and with their ideal value, it is possible toconstruct a system in accordance with the invention using realcomponents, for which the actual angles and retardances will vary fromthese values. One may determine what deviation from these idealizedvalues is acceptable either by mathematical simulation or by directmeasurement and test.

First, consider the configuration of FIG. 1 with a left circularanalyzer and the elliptical polarizer. The elliptical polarizer canexpress one circular and four elliptical polarization states that can beused for capturing the raw images. The positions of the correspondingpolarization states on the Poincare sphere are given in FIG. 3 as _(χ0)through ₁₀₂ ₄, and E₁, E₂, E₃ and E₄ are the vibration ellipses of thesestates.

The Poincare sphere is an established way of representing state ofpolarization, where each point on the sphere indicates a uniquepolarization state of light. The longitude 2θ and latitude 2ε of a pointon the sphere correspond to polarization ellipse with azimuth θ andellipticity angle ε. The ellipticity angle is an auxiliary angle thatspecifies a shape of the vibration ellipse, via the equation tan ε=b/a,where a and b are the major and minor semi-axes of the ellipse. Thus,lines of constant longitude and latitude on the sphere representcontours of equal azimuth and equal ellipticity, respectively. TheNorthern hemisphere indicates light with right-hand ellipticalpolarization, and the Southern hemisphere shows left-hand ellipticallypolarized light.

Some examples of this are as follows. Right and left circularpolarizations correspond to the North Pole and South Pole of the sphere.Each point on the equator represents a distinct linear state ofpolarization, more specifically, a point with longitude 2θ on theequator corresponds to a linear polarization state with azimuth angle θ;while a point in the north hemisphere having same the longitude but withlatitude 2ε corresponds to a right-hand elliptically polarized statewith the same azimuth angle with an ellipticity angle ε.

The extinction setting of the elliptical polarizer when there is nosample retardance corresponds to the North Pole of the sphere. Pointsthat lie on a cone with axis 0Z and the same latitude angle 90°−αdescribe additional settings χ₁, χ₂, χ₃ and χ₄ with longitude angles of0°, 180°, 90° and 270° respectively.

These states χ₀ through χ₄, shown in FIG. 3, are appropriate forpracticing the present invention when used in concert with a leftcircular analyzer. In an analogous manner, one may use an ellipticalpolarizer to generate a set of elliptical states located similarly aboutthe South Pole of the Poincare sphere together with a right circularanalyzer.

Moreover, one can also use polarization states similar to the χ_(1–χ) ₄just described, except that the longitude on the Poincare sphere isshifted by an angle x in each case. This is equivalent to a coordinatetransformation where the azimuth angle is rotated by an angle of x/2.Here and throughout this application, we will treat the case where x=0,but the alternatives with non-zero x work equally well, provided thatone corrects the azimuth angles appropriately by x/2 if they are used.

In order to produce the necessary polarization states in theillumination beam we can use a linear polarizer to produce linearlypolarized light along an axis of 0°, together with a pair of variableretarder plates with various angles between the slow axes. Examples oftwo configurations are shown in FIGS. 1 and 2. In the first case of FIG.1, suitable polarization states can be obtained by the followingsettings of plates 114 and 115:χ₀(90°, 180°),   [1a]χ₁(90°−c, 180°),   [1b]χ₂(90°+c, 180°),   [1c]χ₃(90°, 180°−c),   [1d]χ₄(90°, 180°+c)   [1e]where the notation (α°, β°) denotes that the first waveplate 114 has aretardation of a degrees and the second waveplate 115 has a retardationof β degrees. These comprise a circular polarization state, and fourstates lying at constant latitude of 90°−c on the Poincare sphere,equally spaced in longitude.

In the second configuration of FIG. 2, the angle between slow axes is22.5°. For this case we obtain the same polarization states withsettings:χ₀(270°, 0°),   [2a]χ₁(270°−c, 0°),   [2b]χ₂(270°+c, 0°),   [2c]χ₃(90°−c, 180°),   [2d]χ₄(90°+c, 180°)   [2e]

Like the previous case, these also comprise a circular polarizationstate χ₀ and four equally spaced states χ₁–χ₄ having constant latitudeof 90°−c on the Poincare sphere.

These settings are shown in tabular form in FIG. 4 for the apparatus ofFIGS. 1 and 2. As will be apparent to those skilled in the art, thereare equivalent retarder arrangements that accomplish the same opticalfunction, namely the formation of a polarization analyzer that selectsfor the chosen states of polarization. Such alternative may be employedif desired, without altering the function of the present invention.

The invention provides for using N states from among the five states χ₀through χ₄, where N may be 2, 3, 4, or 5, depending on the requirementsat hand. The invention is thus a more general set of algorithms thatcomplement the 4-state algorithm described in the Oldenbourg and MeiU.S. Pat. No. 5,521,705. These algorithms are now discussed in turn.

Embodiment with N=2

In one preferred embodiment, N=2 and the states used are χ₁ and χ₃.Images are obtained under these conditions with the sample present, andwith no sample. The latter are termed background images, and are used tocompensate for residual polarization signature of the apparatus. Thequantities A and B are calculated from these as follows:A≡(I ₁ −I _(BG1))/I_(BG1)*tan (c/2)  [3a]B≡(I ₃ −I _(BG3))/I_(BG3)*tan (c/2)  [3b]

Here and throughout the remainder of this application, c is perEquations 1a–1e or 2a–2e, I_(i) indicates that the elliptical polarizerwas set to state χ_(i) for that measurement, and the subscript BGindicates a background image, taken with no sample present. From A and Bthe retardance δ and azimuth angle Φ are calculated as:δ=arcsin ([A²+B²]^(1/2))  [4a]Φ=½ arctan (A/B)  [4b]

This embodiment exhibits the best speed, since it requires the leasttime for image acquisition. But its sensitivity is lower than with theother embodiments of the invention where N=3, 4, or 5. It also requiresthat the sample transmission be essentially unity; as absorption in thesample will distort the retardance readings.

An alternative, shown in FIG. 5 in flowchart form, involves taking anadditional background reading with the elliptical polarizer set for theextinction case, i.e. circularly polarized light. The reading thusobtained is termed I_(BG0), and the A and B parameters are calculatedusing the following equations:A≡[(I ₁ −I _(BG1))/(I _(BG1) −I _(BG0))]*tan (c/2)  [4c]B≡[(I ₃ −I _(BG3))/(I _(BG3) −I _(BG0))]*tan (c/2)  [4d]from which δ and Φ are calculated using equations [4a] and [4b].Embodiment with N=3

In a second embodiment, N=3 and the states used are χ₁, χ₂, and χ₃. Fromthe images, one derives the quantities:A≡[(I ₁ −I ₃)/(I ₁ +I ₂)]*tan (c/2)  [5a]B≡[(I ₂ −I ₃)/(I ₁ +I ₂)]*tan (c/2)  [5b]from which the retardance δ and azimuth angle Φ are calculated as:δ=2arctan {[2^(1/2) Z]/[1+(1−2[Z/tan (c/2)]²)^(1/2)]}  [6a]Φ=½arctan (A/B)−22.5°  [6b]whereZ=(A ² +B ²)^(1/2)  [6c]

This embodiment provides better signal-to-noise than the N=2 embodiment,and works well in situations where the optical equipment has a highextinction ratio, such as 200:1 or better.

Embodiment with N=5

In a third embodiment, N=5. All states are used, χ₀–χ₄, to obtain imagesI₀–I₄. From these, one determines the quantities A and B asA≡[(I ₁ −I ₂)/(I ₁ +I ₂−2I ₀)]*tan (c/2)  [7a]B≡[(I ₄ −I ₃)/(I ₄ +I ₃−2I ₀)]*tan (c/2)  [7b]from which the retardance δ and azimuth φ are calculated asδ=arctan (Z) when I ₁ +I ₂−2I ₀≧0  [8a]δ=180°arctan (Z) when (I ₁ +I ₂−2I ₀<0  [8b]Φ=½arctan (A/B)  [8c]

This embodiment has the highest sensitivity of all the embodiments, andhas equal sensitivity for all retardance azimuth values.

Embodiment with N=4

In a fourth embodiment, N=4. The extinction state χ₀ is not used.Instead, the four states used are χ₁, χ₂, χ₃, and χ₄, resulting inimages I₁–I₄. From these, the parameters A and B are calculated as:A=[(I ₁ −I ₂)/(I ₁ +I ₂)] tan(c/2)  [9a]B=[(I ₄ −I ₃)/(I ₄ +I ₃)] tan(c/2)  [9b]from which the retardance δ and azimuth angle Φ are calculated as:δ=2arctan (Z/[1+(1−[Z/ tan (c/2)]²)^(1/2)])  [10a]Φ=½arctan (A/B)  [10b]

This system offers good sensitivity and, like the previous embodiment,the retardance sensitivity is independent of azimuth angle. However, itrequires that the optical apparatus have a high extinction, such as200:1, for best performance.

For any of the above embodiments that omit one or more of the statesχ₁-χ₄, there are equivalent alternatives that can be used equally well.For example, instead of using χ₁ and χ₃, one might use χ₃ and χ₂, or χ₂and χ₄, and so on. These variations consist of the embodiments describedabove, except that the elliptical polarizers express states that areshifted on the Poincare sphere by some fixed longitude shift amount x.As noted earlier, this effects a coordinate transformation of x/2 in theresulting azimuth angle, which can be corrected for if desired.

Similarly, one can construct the elliptical polarizers using variouscombinations of waveplates and polarizers to produce the desired states,rather than using liquid crystal elements. This is an acceptablealternative to the use of liquid crystal retarders, and may be preferredif one wishes to construct apparatus for use in the infrared orultraviolet spectral range, where the performance of liquid crystalretarders may not be high.

It is possible to assemble polarizers which express the required states,and to then cycle them into the optical path using mechanical switchingmeans such as a filter wheel or slider. Alternatively, in embodimentsthat do not make use of χ₀, one may simply rotate the axis of a singleelliptical polarizer to produce the desired states, since χ₁-χ₄ all havethe same degree of ellipticity and differ only in their azimuth angle.

Another alternative is to construct the invention using other types ofelectro-optic elements than liquid crystal retarders, such as Pockelscells, Faraday elements, and the like. Such modifications are explicitlyintended to lie within the scope of the invention, and the constructionof alternative elliptical polarizer apparatus will be understood bythose skilled in the art of polarized optics and of instrument design.Indeed any element may be used to construct the elliptical polarizersprovided that they achieve the desired polarization states, and thatthey suit the application at hand; the choice of one element overanother can be made in terms of such factors as optical performance,aperture, cost, availability, and so on.

In all of the above embodiments, from N=2 through N=5, it is possible toutilize background measurements taken with the sample out to improve themeasurement by correcting for instrumental polarization artifacts. To doso, one records the intensity that is obtained in each polarizer settingwith no sample, and saves these background images. The background imagesneed only be taken at intervals, and may be used to correct any numberof sample images. Typically, they are taken when one expects that theapparatus may have drifted, such as due to a thermal change, or whenusing a different optical set-up such as a different objective lens.

The sequence for recording and utilizing background images is detailedin FIGS. 5 through 11, in flowchart format.

Thus while specific embodiments have been shown, it is understood thatalternatives and equivalent constructions are possible, and that theinvention can be used together with a variety of imaging systems, and incombination with image processing and data analysis techniques, as willbe known by those skilled in these arts. Moreover, while there haveshown and described and pointed out fundamental novel features of theinvention as applied to preferred embodiments thereof, it will beunderstood that various omissions and substitutions and changes in theform and details of the methods described and devices illustrated, andin their operation, may be made by those skilled in the art withoutdeparting from the spirit of the invention. For example, it is expresslyintended that all combinations of those elements and/or method stepswhich perform substantially the same function in substantially the sameway to achieve the same results are within the scope of the invention.In addition, it should be recognized that structures and/or elementsand/or method steps shown and/or described in connection with anydisclosed form or embodiment of the invention may be incorporated in anyother disclosed or described or suggested form or embodiment as ageneral matter of design choice. It is the intention, therefore, to belimited only as indicated by the scope of the claims appended hereto.

1. An apparatus for measuring retardance in a sample, comprising: asample chamber for receiving the sample; an illuminator for providing anillumination light; optics for directing the illumination light towardthe sample; a detector for measuring an intensity of light incident onthe detector; optics for directing light that has interacted with thesample toward the detector; a first polarizer for selectivelytransmitting light that is substantially circularly polarized; a secondpolarizer for selectively transmitting light that has a selectedelliptical polarization state; a controller for varying a selectedelliptical polarization state of the second polarizer to correspond to aplural number of states χ_(i) with a chosen Poincare latitude andlongitude within a distance ε of a chosen pole of a Poincare sphere; anda processor connected to the detector for determining the sampleretardance from the measured incident light intensity obtained when thesecond polarizer is set to each of the states χ_(i); wherein none of thestates χ_(i) corresponds to circular polarization.
 2. The apparatus ofclaim 1, wherein the illumination light is transmitted by the sample. 3.The apparatus of claim 1, wherein the illumination light is reflected bythe sample.
 4. The apparatus of claim 1, wherein: the first polarizer islocated between the illuminator and the sample chamber; and the secondpolarizer is located between the sample chamber and the detector.
 5. Theapparatus of claim 1, wherein: the second polarizer is located betweenthe illuminator and the sample chamber; and the first polarizer islocated between the sample chamber and the detector.
 6. The apparatus ofclaim 1, wherein the number of states χ_(i) is
 2. 7. The apparatus ofclaim 1, wherein the number of states χ_(i) is
 3. 8. The apparatus ofclaim 1, wherein the number of states χ_(i) is
 4. 9. The apparatus ofclaim 1, wherein the second polarizer comprises an electro-opticretarder element.
 10. The apparatus of claim 1, wherein the secondpolarizer comprises at least one fixed retarder and mechanical switchingmeans.
 11. The apparatus of claim 1, wherein the illumination light issubstantially monochromatic.
 12. The apparatus of claim 1, wherein theilluminator comprises a broadband source and a filter.
 13. The apparatusof claim 1, wherein ε is 35 degrees or less.
 14. The apparatus of claim1, wherein ε is 20 degrees or less.
 15. A method for measuringretardance in a sample in a sample chamber, comprising the steps of:producing an illumination beam of light; directing the illumination beamtoward the sample; collecting directed illumination light that hasinteracted with the sample to form a collected light beam; directing thecollected light beam toward a photodetector; directing one of theillumination beam and the collected light beam through a circularpolarizer; directing the other of the illumination beam and thecollected light beam through a variable polarizer that expresses aplural number of elliptical polarization states χ_(i); measuring anintensity of light incident on the photodetector during each of theplural states χ_(i); and calculating the retardance of the sample usingthe photodetector light intensity measurements; wherein the number ofstates χ_(i) is four or less and none of the states χ_(i) is circular.16. The method of claim 15, wherein each of the plural states χ_(i) lieswithin a distance ε from a chosen pole of the Poincare sphere.
 17. Themethod of claim 16, wherein ε is 35 degrees or less.
 18. The method ofclaim 16, wherein ε is 20 degrees or less.
 19. The method of claim 15,further comprising the steps of: measuring the intensity of lightincident on the photodetector while the variable polarizer expresses aplurality of states χ_(i) and the sample is not present in the samplechamber; and using the measured intensities of light incident on thephotodetector when the sample is not present to improve the calculationof sample retardance.
 20. The method of claim 19, wherein said measuringthe intensity of light with the sample not present in the sample chambercomprises measuring the light intensity with the sample replaced by acalibration target of substantially no retardance and a calibrationtarget of known retardance.